Question

4. A needle 10 cm long is placed along the axis of principle axis of a convex lens of focal
length 10cm such that its mid point is at distance 20cm from the lens. Find the length of
image of needle. (Va=+30cm, Vb=16.67cm)​

Answer 1

The length of image of needle is 13.33 cm.

Explanation:

Given that,

Length of needle = 10 cm

Focal length = 10 cm

Object distance = 20 cm

We need to calculate the distance of needle from the lens

Using to figure,

AC = 20-5= 15 cm

BC=20+5= 25 m

We need to calculate the distance of image of needle of A

Using formula of lens

$\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}$

Put the value into the formula

$\dfrac{1}{10}=\dfrac{1}{v_{a}}+\dfrac{1}{15}$

$\dfrac{1}{v_{a}}=\dfrac{1}{10}-\dfrac{1}{15}$

$v=30\ cm$

We need to calculate the distance of image of needle of B

Using formula of lens

$\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}$

Put the value into the formula

$\dfrac{1}{10}=\dfrac{1}{v_{b}}+\dfrac{1}{25}$

$\dfrac{1}{v_{b}}=\dfrac{1}{10}-\dfrac{1}{25}$

$\dfrac{1}{v_{b}}=\dfrac{3}{50}$

$v_{b}=16.67\ cm$

We need to calculate the length of image of needle

Using formula of distance of image

$L_{i}=v_{a}-v_{b}$

Put the value into the formula

$L_{i}=30-16.67$

$L_{i}=13.33\ cm$

Hence, The length of image of needle is 13.33 cm.

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Topic : optics

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